Feldstein, money, inflation and the zero bound

I just came across this by Marty Feldstein, circulated by Matt O Brien on Twitter.  And it's mighty confusing.  The premise of the article is the puzzle that the rapid expansion of the monetary base since the onset of the financial crisis was not accompanied by the historically normal corresponding increase in prices. But why should this be such a puzzle?  Standard models of money demand predict that as the cost of holding real money balances [that's money divided by prices] falls, the demand for them rises.  This requires assuming that real balances have some use, and for sure many are still justly pondering just what that is, but I doubt that Feldstein would depart from the holding answers we have developed thus far. So during any period when nominal interest rates fall sharply, we would not expect money and prices to move one for one because real balances will increase.

Moreover, notice that what has happened is that base money has expanded while interest rates have been at, approximately, the zero bound.  The same standard model supposes that the market for real balances clears.  And that interest rates at the zero bound implies that the amount of usefulness yielded by the last increment in real balances has also fallen to zero or thereabouts.  Implying, given how we normally assume that this increment falls as real balances increases, but by less each time, that real balances are tending to infinity.  Taking the model literally, there's no reason to expect the price level to move at all with the expansion of money.  [This is a crude version of the story told by Krugman and later Eggertson and Woodford].

Go back a few years, and you will see that Feldstein edited an NBER book of papers explaining the 'costs of inflation'.  And the fulcrum of this work is the deadweight loss imposed on society when high inflation, and corresponding high nominal interest rates in the steady state [courtesy of the Fisher effect], causes people to cut back on real balances.  Which, since these balances are assumed to be socially useful, is costly.

So the key to Feldstein's puzzle is in his earlier work on the costs of inflation.  Just reasoning the other way along the demand curve for real balances.